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          GNN for Source Code Modeling（三）
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        <p>实际上 GNN 在 Source Code 上的应用和创新还有很多。之前的两篇文章都是关于 GNN 建图以及 GNN 跟其他任务相结合的工作，这篇文章就讲一下对 GNN 本身的创新。</p>
<span id="more"></span>
<p><a target="_blank" rel="noopener" href="https://arxiv.org/abs/1904.12787">Graph Matching Networks for Learning the Similarity of Graph Structured Objects. ICML 2019</a> 就是一个利用 GNN 解决二进制函数相似性问题的工作。这个问题也是 Source Code Modeling 领域的经典问题之一。 二进制函数相似性是一个在信息安全领域应用很广泛的问题。因为很多软件都是不开源的，放在用户电脑上的只能是一些二进制代码。因为编译器、编译选项以及平台的不同，同一个函数的二进制代码也经常是不同的。如果一个函数被检查出了安全漏洞，那这个函数所编译出的所有二进制代码也会有安全漏洞。这些二进制代码放在成千上万用户的电脑上，造成非常大的安全隐患，所以及时找到这些代码是非常重要的。因为二进制代码本身会有一个 Control-flow-graph，所以利用 GNN 解决二进制函数相似性就成为 GNN 的一个应用。</p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/1-1.png"></p>
<p>论文中给出两种方式来解决这个问题。第一种是输入一个图输出一个 embedding，通过优化这个 embedding 使得两个相似的图的 embedding 会离得更近。第二种更加直接，输入两个图，输出他们的相似性。这两种方式都是在 GNN 的基础上做的。</p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/2-1.png"></p>
<p>第一种方法计算 embedding 的过程没啥好说的，就是输入<span class="math inline">\((G_1, G_2)\)</span>输出<span class="math inline">\((h_{G_1},h_{G_2})\)</span>。重点在于最后的 loss 设计，因为跟第二种可以共用相同的 loss，所以放到一起最后讲。 对于第二种方法，大多数步骤跟 GNN 都是一样的。主要区别在于在聚合邻居信息的时候，也要聚合另一张图的信息 <span class="math inline">\(\mu\)</span>：</p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/3-1.png"></p>
<p>其中<span class="math inline">\(\mu\)</span>的计算方式如下，上面的<span class="math inline">\(f_s\)</span>和下面的<span class="math inline">\(s_h\)</span>都是可以替换的向量相似度计算方式：</p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/4-1.png"></p>
<p>观察公式<span class="math inline">\((11)\)</span>可以发现，attention 值越大，两个点越相似。所以这个<span class="math inline">\(\Sigma\mu\)</span>其实就是该点的 embedding 跟另一张图最相似的点的 embedding 的差。如果两个图完全一样，那这个<span class="math inline">\(\Sigma\mu\)</span>就会一直是<span class="math inline">\(0\)</span>。所以这个 GMN 的优势就是通过一个图的表示可以更改另一个图的表示，从而捕捉两个图的不相似程度。 下面是两种方法的 loss。论文定义了两种 label，第一种是<span class="math inline">\((G_1,G_2,t)\)</span>，两个图相似<span class="math inline">\(t=1\)</span>，不相似<span class="math inline">\(t=-1\)</span>。第二种是<span class="math inline">\((G_1,G_2,G_3)\)</span>，其中<span class="math inline">\(G_1\)</span>跟<span class="math inline">\(G_2\)</span>更加相似。如果向量相似性用欧拉距离来度量，那可以用一种类似合页 loss 的方式来进行优化：</p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/5-1.png"></p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/6-1.png"></p>
<p>公式<span class="math inline">\((12)\)</span>可以看做当两个图相似的时候，距离应该小于<span class="math inline">\(1-\gamma\)</span>，当两个图不相似的时候，距离应该大于<span class="math inline">\(1+\gamma\)</span>。 公式<span class="math inline">\((13)\)</span>可以看做<span class="math inline">\(d(G_1,G_2)\lt d(G_1,G_3)-\gamma\)</span>。</p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/7-1.png"> 也可以按照上面的公式，用 Hamming 相似度来算，这样的好处是向量里面每一维度都是<span class="math inline">\([1,-1]\)</span>，容易在大型数据库中快速的查询。</p>
<p><img src="/2020/03/09/gnn-for-source-code-modeling-3/8-1.png"></p>
<p>可以看到，效果有一定的提升。这里的 baseline 是 Google 的一个二进制代码查询工具，利用手工构造的图 hash 来寻找相同的代码。</p>

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